LMFDB - Embedded newform 735.2.a.o.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(1,735)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("735.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.4352.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} - 4x + 2 $ x^4 - 6x^2 - 4x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.68554$ of defining polynomial
Character	$\chi$	$=$	735.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.27133 q^{2} +1.00000 q^{3} +3.15894 q^{4} -1.00000 q^{5} +2.27133 q^{6} +2.63234 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.27133 q^{2} +1.00000 q^{3} +3.15894 q^{4} -1.00000 q^{5} +2.27133 q^{6} +2.63234 q^{8} +1.00000 q^{9} -2.27133 q^{10} +5.05320 q^{11} +3.15894 q^{12} +0.224777 q^{13} -1.00000 q^{15} -0.338971 q^{16} -3.59587 q^{17} +2.27133 q^{18} +4.78530 q^{19} -3.15894 q^{20} +11.4775 q^{22} +7.01008 q^{23} +2.63234 q^{24} +1.00000 q^{25} +0.510544 q^{26} +1.00000 q^{27} -8.74218 q^{29} -2.27133 q^{30} -8.78530 q^{31} -6.03459 q^{32} +5.05320 q^{33} -8.16740 q^{34} +3.15894 q^{36} -5.91375 q^{37} +10.8690 q^{38} +0.224777 q^{39} -2.63234 q^{40} -8.42429 q^{41} -4.31788 q^{43} +15.9628 q^{44} -1.00000 q^{45} +15.9222 q^{46} +10.4853 q^{47} -0.338971 q^{48} +2.27133 q^{50} -3.59587 q^{51} +0.710059 q^{52} +0.361009 q^{53} +2.27133 q^{54} -5.05320 q^{55} +4.78530 q^{57} -19.8564 q^{58} +6.25689 q^{59} -3.15894 q^{60} -6.58579 q^{61} -19.9543 q^{62} -13.0286 q^{64} -0.224777 q^{65} +11.4775 q^{66} -8.36330 q^{67} -11.3591 q^{68} +7.01008 q^{69} -12.9670 q^{71} +2.63234 q^{72} +4.86054 q^{73} -13.4321 q^{74} +1.00000 q^{75} +15.1165 q^{76} +0.510544 q^{78} +2.88942 q^{79} +0.338971 q^{80} +1.00000 q^{81} -19.1344 q^{82} +12.8284 q^{83} +3.59587 q^{85} -9.80734 q^{86} -8.74218 q^{87} +13.3017 q^{88} -4.82843 q^{89} -2.27133 q^{90} +22.1444 q^{92} -8.78530 q^{93} +23.8155 q^{94} -4.78530 q^{95} -6.03459 q^{96} -2.48167 q^{97} +5.05320 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 8 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 8 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} + 4 q^{3} + 8 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{8} + 4 q^{9} - 4 q^{10} + 8 q^{11} + 8 q^{12} - 4 q^{15} + 12 q^{16} + 8 q^{17} + 4 q^{18} - 8 q^{19} - 8 q^{20} + 12 q^{24} + 4 q^{25} + 4 q^{27} + 8 q^{29} - 4 q^{30} - 8 q^{31} + 28 q^{32} + 8 q^{33} - 8 q^{34} + 8 q^{36} + 8 q^{37} + 4 q^{38} - 12 q^{40} - 8 q^{43} - 16 q^{44} - 4 q^{45} + 12 q^{46} + 8 q^{47} + 12 q^{48} + 4 q^{50} + 8 q^{51} - 32 q^{52} + 8 q^{53} + 4 q^{54} - 8 q^{55} - 8 q^{57} - 24 q^{58} + 16 q^{59} - 8 q^{60} - 32 q^{61} - 20 q^{62} + 24 q^{64} + 24 q^{68} - 8 q^{71} + 12 q^{72} - 32 q^{74} + 4 q^{75} + 8 q^{76} - 12 q^{80} + 4 q^{81} - 8 q^{82} + 40 q^{83} - 8 q^{85} - 32 q^{86} + 8 q^{87} - 40 q^{88} - 8 q^{89} - 4 q^{90} - 8 q^{92} - 8 q^{93} - 16 q^{94} + 8 q^{95} + 28 q^{96} + 8 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 8 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^8 + 4 * q^9 - 4 * q^10 + 8 * q^11 + 8 * q^12 - 4 * q^15 + 12 * q^16 + 8 * q^17 + 4 * q^18 - 8 * q^19 - 8 * q^20 + 12 * q^24 + 4 * q^25 + 4 * q^27 + 8 * q^29 - 4 * q^30 - 8 * q^31 + 28 * q^32 + 8 * q^33 - 8 * q^34 + 8 * q^36 + 8 * q^37 + 4 * q^38 - 12 * q^40 - 8 * q^43 - 16 * q^44 - 4 * q^45 + 12 * q^46 + 8 * q^47 + 12 * q^48 + 4 * q^50 + 8 * q^51 - 32 * q^52 + 8 * q^53 + 4 * q^54 - 8 * q^55 - 8 * q^57 - 24 * q^58 + 16 * q^59 - 8 * q^60 - 32 * q^61 - 20 * q^62 + 24 * q^64 + 24 * q^68 - 8 * q^71 + 12 * q^72 - 32 * q^74 + 4 * q^75 + 8 * q^76 - 12 * q^80 + 4 * q^81 - 8 * q^82 + 40 * q^83 - 8 * q^85 - 32 * q^86 + 8 * q^87 - 40 * q^88 - 8 * q^89 - 4 * q^90 - 8 * q^92 - 8 * q^93 - 16 * q^94 + 8 * q^95 + 28 * q^96 + 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.27133	1.60607	0.803037	−	0.595930i	$-0.203216\pi$
$2$	2.27133	1.60607	0.803037	+	0.595930i	$0.203216\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.15894	1.57947
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.27133	0.927267
$7$	0	0
$7$	0	0
$8$	2.63234	0.930673
$9$	1.00000	0.333333
$10$	−2.27133	−0.718258
$11$	5.05320	1.52360	0.761799	−	0.647813i	$-0.224316\pi$
$11$	5.05320	1.52360	0.761799	+	0.647813i	$0.224316\pi$
$12$	3.15894	0.911908
$13$	0.224777	0.0623420	0.0311710	−	0.999514i	$-0.490076\pi$
$13$	0.224777	0.0623420	0.0311710	+	0.999514i	$0.490076\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	−0.338971	−0.0847427
$17$	−3.59587	−0.872125	−0.436063	−	0.899916i	$-0.643627\pi$
$17$	−3.59587	−0.872125	−0.436063	+	0.899916i	$0.643627\pi$
$18$	2.27133	0.535358
$19$	4.78530	1.09782	0.548912	−	0.835880i	$-0.315042\pi$
$19$	4.78530	1.09782	0.548912	+	0.835880i	$0.315042\pi$
$20$	−3.15894	−0.706361
$21$	0	0
$22$	11.4775	2.44701
$23$	7.01008	1.46170	0.730851	−	0.682537i	$-0.239123\pi$
$23$	7.01008	1.46170	0.730851	+	0.682537i	$0.239123\pi$
$24$	2.63234	0.537324
$25$	1.00000	0.200000
$26$	0.510544	0.100126
$27$	1.00000	0.192450
$28$	0	0
$29$	−8.74218	−1.62338	−0.811691	−	0.584088i	$-0.801452\pi$
$29$	−8.74218	−1.62338	−0.811691	+	0.584088i	$0.801452\pi$
$30$	−2.27133	−0.414686
$31$	−8.78530	−1.57789	−0.788943	−	0.614466i	$-0.789372\pi$
$31$	−8.78530	−1.57789	−0.788943	+	0.614466i	$0.789372\pi$
$32$	−6.03459	−1.06678
$33$	5.05320	0.879650
$34$	−8.16740	−1.40070
$35$	0	0
$36$	3.15894	0.526490
$37$	−5.91375	−0.972214	−0.486107	−	0.873899i	$-0.661584\pi$
$37$	−5.91375	−0.972214	−0.486107	+	0.873899i	$0.661584\pi$
$38$	10.8690	1.76318
$39$	0.224777	0.0359932
$40$	−2.63234	−0.416209
$41$	−8.42429	−1.31565	−0.657827	−	0.753169i	$-0.728524\pi$
$41$	−8.42429	−1.31565	−0.657827	+	0.753169i	$0.728524\pi$
$42$	0	0
$43$	−4.31788	−0.658471	−0.329236	−	0.944248i	$-0.606791\pi$
$43$	−4.31788	−0.658471	−0.329236	+	0.944248i	$0.606791\pi$
$44$	15.9628	2.40648
$45$	−1.00000	−0.149071
$46$	15.9222	2.34760
$47$	10.4853	1.52944	0.764718	−	0.644365i	$-0.222878\pi$
$47$	10.4853	1.52944	0.764718	+	0.644365i	$0.222878\pi$
$48$	−0.338971	−0.0489262
$49$	0	0
$50$	2.27133	0.321215
$51$	−3.59587	−0.503522
$52$	0.710059	0.0984674
$53$	0.361009	0.0495884	0.0247942	−	0.999693i	$-0.492107\pi$
$53$	0.361009	0.0495884	0.0247942	+	0.999693i	$0.492107\pi$
$54$	2.27133	0.309089
$55$	−5.05320	−0.681374
$56$	0	0
$57$	4.78530	0.633829
$58$	−19.8564	−2.60727
$59$	6.25689	0.814578	0.407289	−	0.913299i	$-0.366474\pi$
$59$	6.25689	0.814578	0.407289	+	0.913299i	$0.366474\pi$
$60$	−3.15894	−0.407818
$61$	−6.58579	−0.843224	−0.421612	−	0.906776i	$-0.638535\pi$
$61$	−6.58579	−0.843224	−0.421612	+	0.906776i	$0.638535\pi$
$62$	−19.9543	−2.53420
$63$	0	0
$64$	−13.0286	−1.62858
$65$	−0.224777	−0.0278802
$66$	11.4775	1.41278
$67$	−8.36330	−1.02174	−0.510870	−	0.859658i	$-0.670677\pi$
$67$	−8.36330	−1.02174	−0.510870	+	0.859658i	$0.670677\pi$
$68$	−11.3591	−1.37750
$69$	7.01008	0.843914
$70$	0	0
$71$	−12.9670	−1.53889	−0.769447	−	0.638711i	$-0.779468\pi$
$71$	−12.9670	−1.53889	−0.769447	+	0.638711i	$0.779468\pi$
$72$	2.63234	0.310224
$73$	4.86054	0.568884	0.284442	−	0.958693i	$-0.408192\pi$
$73$	4.86054	0.568884	0.284442	+	0.958693i	$0.408192\pi$
$74$	−13.4321	−1.56145
$75$	1.00000	0.115470
$76$	15.1165	1.73398
$77$	0	0
$78$	0.510544	0.0578077
$79$	2.88942	0.325085	0.162542	−	0.986702i	$-0.448031\pi$
$79$	2.88942	0.325085	0.162542	+	0.986702i	$0.448031\pi$
$80$	0.338971	0.0378981
$81$	1.00000	0.111111
$82$	−19.1344	−2.11304
$83$	12.8284	1.40810	0.704051	−	0.710149i	$-0.251372\pi$
$83$	12.8284	1.40810	0.704051	+	0.710149i	$0.251372\pi$
$84$	0	0
$85$	3.59587	0.390026
$86$	−9.80734	−1.05755
$87$	−8.74218	−0.937260
$88$	13.3017	1.41797
$89$	−4.82843	−0.511812	−0.255906	−	0.966702i	$-0.582374\pi$
$89$	−4.82843	−0.511812	−0.255906	+	0.966702i	$0.582374\pi$
$90$	−2.27133	−0.239419
$91$	0	0
$92$	22.1444	2.30872
$93$	−8.78530	−0.910993
$94$	23.8155	2.45639
$95$	−4.78530	−0.490962
$96$	−6.03459	−0.615903
$97$	−2.48167	−0.251976	−0.125988	−	0.992032i	$-0.540210\pi$
$97$	−2.48167	−0.251976	−0.125988	+	0.992032i	$0.540210\pi$
$98$	0	0
$99$	5.05320	0.507866
$100$	3.15894	0.315894
$101$	−1.23256	−0.122644	−0.0613222	−	0.998118i	$-0.519532\pi$
$101$	−1.23256	−0.122644	−0.0613222	+	0.998118i	$0.519532\pi$
$102$	−8.16740	−0.808693
$103$	11.9137	1.17390	0.586948	−	0.809624i	$-0.300329\pi$
$103$	11.9137	1.17390	0.586948	+	0.809624i	$0.300329\pi$
$104$	0.591691	0.0580200
$105$	0	0
$106$	0.819971	0.0796426
$107$	−0.903670	−0.0873611	−0.0436805	−	0.999046i	$-0.513908\pi$
$107$	−0.903670	−0.0873611	−0.0436805	+	0.999046i	$0.513908\pi$
$108$	3.15894	0.303969
$109$	7.65685	0.733394	0.366697	−	0.930341i	$-0.380489\pi$
$109$	7.65685	0.733394	0.366697	+	0.930341i	$0.380489\pi$
$110$	−11.4775	−1.09434
$111$	−5.91375	−0.561308
$112$	0	0
$113$	9.56831	0.900111	0.450055	−	0.893001i	$-0.351404\pi$
$113$	9.56831	0.900111	0.450055	+	0.893001i	$0.351404\pi$
$114$	10.8690	1.01798
$115$	−7.01008	−0.653693
$116$	−27.6160	−2.56408
$117$	0.224777	0.0207807
$118$	14.2115	1.30827
$119$	0	0
$120$	−2.63234	−0.240299
$121$	14.5349	1.32135
$122$	−14.9585	−1.35428
$123$	−8.42429	−0.759593
$124$	−27.7523	−2.49223
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−10.5105	−0.932660	−0.466330	−	0.884611i	$-0.654424\pi$
$127$	−10.5105	−0.932660	−0.466330	+	0.884611i	$0.654424\pi$
$128$	−17.5231	−1.54884
$129$	−4.31788	−0.380168
$130$	−0.510544	−0.0447777
$131$	15.4454	1.34947	0.674735	−	0.738060i	$-0.264258\pi$
$131$	15.4454	1.34947	0.674735	+	0.738060i	$0.264258\pi$
$132$	15.9628	1.38938
$133$	0	0
$134$	−18.9958	−1.64099
$135$	−1.00000	−0.0860663
$136$	−9.46554	−0.811663
$137$	12.5738	1.07425	0.537127	−	0.843501i	$-0.319509\pi$
$137$	12.5738	1.07425	0.537127	+	0.843501i	$0.319509\pi$
$138$	15.9222	1.35539
$139$	−5.32111	−0.451330	−0.225665	−	0.974205i	$-0.572456\pi$
$139$	−5.32111	−0.451330	−0.225665	+	0.974205i	$0.572456\pi$
$140$	0	0
$141$	10.4853	0.883020
$142$	−29.4522	−2.47158
$143$	1.13585	0.0949842
$144$	−0.338971	−0.0282476
$145$	8.74218	0.725998
$146$	11.0399	0.913669
$147$	0	0
$148$	−18.6812	−1.53558
$149$	10.6358	0.871316	0.435658	−	0.900112i	$-0.356516\pi$
$149$	10.6358	0.871316	0.435658	+	0.900112i	$0.356516\pi$
$150$	2.27133	0.185453
$151$	12.4885	1.01630	0.508151	−	0.861268i	$-0.330329\pi$
$151$	12.4885	1.01630	0.508151	+	0.861268i	$0.330329\pi$
$152$	12.5965	1.02171
$153$	−3.59587	−0.290708
$154$	0	0
$155$	8.78530	0.705652
$156$	0.710059	0.0568502
$157$	−9.43208	−0.752762	−0.376381	−	0.926465i	$-0.622832\pi$
$157$	−9.43208	−0.752762	−0.376381	+	0.926465i	$0.622832\pi$
$158$	6.56282	0.522110
$159$	0.361009	0.0286299
$160$	6.03459	0.477077
$161$	0	0
$162$	2.27133	0.178453
$163$	8.04542	0.630166	0.315083	−	0.949064i	$-0.397968\pi$
$163$	8.04542	0.630166	0.315083	+	0.949064i	$0.397968\pi$
$164$	−26.6118	−2.07804
$165$	−5.05320	−0.393391
$166$	29.1376	2.26152
$167$	9.53488	0.737831	0.368915	−	0.929463i	$-0.379729\pi$
$167$	9.53488	0.737831	0.368915	+	0.929463i	$0.379729\pi$
$168$	0	0
$169$	−12.9495	−0.996113
$170$	8.16740	0.626411
$171$	4.78530	0.365941
$172$	−13.6399	−1.04004
$173$	11.0243	0.838164	0.419082	−	0.907948i	$-0.362352\pi$
$173$	11.0243	0.838164	0.419082	+	0.907948i	$0.362352\pi$
$174$	−19.8564	−1.50531
$175$	0	0
$176$	−1.71289	−0.129114
$177$	6.25689	0.470297
$178$	−10.9670	−0.822008
$179$	10.0523	0.751342	0.375671	−	0.926753i	$-0.377412\pi$
$179$	10.0523	0.751342	0.375671	+	0.926753i	$0.377412\pi$
$180$	−3.15894	−0.235454
$181$	12.6417	0.939648	0.469824	−	0.882760i	$-0.344317\pi$
$181$	12.6417	0.939648	0.469824	+	0.882760i	$0.344317\pi$
$182$	0	0
$183$	−6.58579	−0.486835
$184$	18.4529	1.36037
$185$	5.91375	0.434787
$186$	−19.9543	−1.46312
$187$	−18.1706	−1.32877
$188$	33.1224	2.41570
$189$	0	0
$190$	−10.8690	−0.788520
$191$	−21.4522	−1.55223	−0.776115	−	0.630592i	$-0.782812\pi$
$191$	−21.4522	−1.55223	−0.776115	+	0.630592i	$0.782812\pi$
$192$	−13.0286	−0.940259
$193$	−10.4445	−0.751808	−0.375904	−	0.926659i	$-0.622668\pi$
$193$	−10.4445	−0.751808	−0.375904	+	0.926659i	$0.622668\pi$
$194$	−5.63670	−0.404691
$195$	−0.224777	−0.0160966
$196$	0	0
$197$	−15.5885	−1.11063	−0.555316	−	0.831639i	$-0.687403\pi$
$197$	−15.5885	−1.11063	−0.555316	+	0.831639i	$0.687403\pi$
$198$	11.4775	0.815670
$199$	−18.8917	−1.33920	−0.669599	−	0.742723i	$-0.733534\pi$
$199$	−18.8917	−1.33920	−0.669599	+	0.742723i	$0.733534\pi$
$200$	2.63234	0.186135
$201$	−8.36330	−0.589902
$202$	−2.79956	−0.196976
$203$	0	0
$204$	−11.3591	−0.795298
$205$	8.42429	0.588378
$206$	27.0601	1.88536
$207$	7.01008	0.487234
$208$	−0.0761930	−0.00528304
$209$	24.1811	1.67264
$210$	0	0
$211$	20.3990	1.40433	0.702164	−	0.712016i	$-0.252218\pi$
$211$	20.3990	1.40433	0.702164	+	0.712016i	$0.252218\pi$
$212$	1.14041	0.0783234
$213$	−12.9670	−0.888481
$214$	−2.05253	−0.140308
$215$	4.31788	0.294477
$216$	2.63234	0.179108
$217$	0	0
$218$	17.3912	1.17788
$219$	4.86054	0.328445
$220$	−15.9628	−1.07621
$221$	−0.808269	−0.0543701
$222$	−13.4321	−0.901502
$223$	−13.8073	−0.924608	−0.462304	−	0.886722i	$-0.652977\pi$
$223$	−13.8073	−0.924608	−0.462304	+	0.886722i	$0.652977\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	21.7328	1.44564
$227$	1.89359	0.125682	0.0628410	−	0.998024i	$-0.479984\pi$
$227$	1.89359	0.125682	0.0628410	+	0.998024i	$0.479984\pi$
$228$	15.1165	1.00111
$229$	−19.0711	−1.26025	−0.630126	−	0.776493i	$-0.716997\pi$
$229$	−19.0711	−1.26025	−0.630126	+	0.776493i	$0.716997\pi$
$230$	−15.9222	−1.04988
$231$	0	0
$232$	−23.0124	−1.51084
$233$	18.9170	1.23929	0.619646	−	0.784881i	$-0.287276\pi$
$233$	18.9170	1.23929	0.619646	+	0.784881i	$0.287276\pi$
$234$	0.510544	0.0333753
$235$	−10.4853	−0.683984
$236$	19.7652	1.28660
$237$	2.88942	0.187688
$238$	0	0
$239$	4.66788	0.301940	0.150970	−	0.988538i	$-0.451760\pi$
$239$	4.66788	0.301940	0.150970	+	0.988538i	$0.451760\pi$
$240$	0.338971	0.0218805
$241$	−27.4986	−1.77134	−0.885670	−	0.464314i	$-0.846301\pi$
$241$	−27.4986	−1.77134	−0.885670	+	0.464314i	$0.846301\pi$
$242$	33.0135	2.12219
$243$	1.00000	0.0641500
$244$	−20.8041	−1.33185
$245$	0	0
$246$	−19.1344	−1.21996
$247$	1.07563	0.0684406
$248$	−23.1259	−1.46850
$249$	12.8284	0.812969
$250$	−2.27133	−0.143652
$251$	1.62113	0.102325	0.0511623	−	0.998690i	$-0.483707\pi$
$251$	1.62113	0.102325	0.0511623	+	0.998690i	$0.483707\pi$
$252$	0	0
$253$	35.4234	2.22705
$254$	−23.8729	−1.49792
$255$	3.59587	0.225182
$256$	−13.7435	−0.858970
$257$	−8.10641	−0.505664	−0.252832	−	0.967510i	$-0.581362\pi$
$257$	−8.10641	−0.505664	−0.252832	+	0.967510i	$0.581362\pi$
$258$	−9.80734	−0.610578
$259$	0	0
$260$	−0.710059	−0.0440360
$261$	−8.74218	−0.541127
$262$	35.0816	2.16735
$263$	−4.63121	−0.285572	−0.142786	−	0.989754i	$-0.545606\pi$
$263$	−4.63121	−0.285572	−0.142786	+	0.989754i	$0.545606\pi$
$264$	13.3017	0.818666
$265$	−0.361009	−0.0221766
$266$	0	0
$267$	−4.82843	−0.295495
$268$	−26.4192	−1.61381
$269$	6.61695	0.403443	0.201721	−	0.979443i	$-0.435346\pi$
$269$	6.61695	0.403443	0.201721	+	0.979443i	$0.435346\pi$
$270$	−2.27133	−0.138229
$271$	−12.6633	−0.769242	−0.384621	−	0.923075i	$-0.625668\pi$
$271$	−12.6633	−0.769242	−0.384621	+	0.923075i	$0.625668\pi$
$272$	1.21889	0.0739063
$273$	0	0
$274$	28.5593	1.72533
$275$	5.05320	0.304720
$276$	22.1444	1.33294
$277$	11.1665	0.670928	0.335464	−	0.942053i	$-0.391107\pi$
$277$	11.1665	0.670928	0.335464	+	0.942053i	$0.391107\pi$
$278$	−12.0860	−0.724870
$279$	−8.78530	−0.525962
$280$	0	0
$281$	25.9495	1.54802	0.774008	−	0.633176i	$-0.218249\pi$
$281$	25.9495	1.54802	0.774008	+	0.633176i	$0.218249\pi$
$282$	23.8155	1.41819
$283$	16.1266	0.958625	0.479312	−	0.877644i	$-0.340886\pi$
$283$	16.1266	0.958625	0.479312	+	0.877644i	$0.340886\pi$
$284$	−40.9618	−2.43064
$285$	−4.78530	−0.283457
$286$	2.57988	0.152552
$287$	0	0
$288$	−6.03459	−0.355592
$289$	−4.06975	−0.239397
$290$	19.8564	1.16601
$291$	−2.48167	−0.145478
$292$	15.3542	0.898535
$293$	22.3990	1.30857	0.654283	−	0.756250i	$-0.272971\pi$
$293$	22.3990	1.30857	0.654283	+	0.756250i	$0.272971\pi$
$294$	0	0
$295$	−6.25689	−0.364290
$296$	−15.5670	−0.904813
$297$	5.05320	0.293217
$298$	24.1573	1.39940
$299$	1.57571	0.0911255
$300$	3.15894	0.182382
$301$	0	0
$302$	28.3656	1.63226
$303$	−1.23256	−0.0708088
$304$	−1.62208	−0.0930326
$305$	6.58579	0.377101
$306$	−8.16740	−0.466899
$307$	−15.3137	−0.874000	−0.437000	−	0.899462i	$-0.643959\pi$
$307$	−15.3137	−0.874000	−0.437000	+	0.899462i	$0.643959\pi$
$308$	0	0
$309$	11.9137	0.677749
$310$	19.9543	1.13333
$311$	4.71691	0.267472	0.133736	−	0.991017i	$-0.457303\pi$
$311$	4.71691	0.267472	0.133736	+	0.991017i	$0.457303\pi$
$312$	0.591691	0.0334979
$313$	−21.4724	−1.21369	−0.606846	−	0.794820i	$-0.707565\pi$
$313$	−21.4724	−1.21369	−0.606846	+	0.794820i	$0.707565\pi$
$314$	−21.4234	−1.20899
$315$	0	0
$316$	9.12750	0.513462
$317$	−3.76097	−0.211237	−0.105619	−	0.994407i	$-0.533682\pi$
$317$	−3.76097	−0.211237	−0.105619	+	0.994407i	$0.533682\pi$
$318$	0.819971	0.0459817
$319$	−44.1760	−2.47338
$320$	13.0286	0.728322
$321$	−0.903670	−0.0504379
$322$	0	0
$323$	−17.2073	−0.957440
$324$	3.15894	0.175497
$325$	0.224777	0.0124684
$326$	18.2738	1.01209
$327$	7.65685	0.423425
$328$	−22.1756	−1.22444
$329$	0	0
$330$	−11.4775	−0.631815
$331$	3.42847	0.188446	0.0942228	−	0.995551i	$-0.469963\pi$
$331$	3.42847	0.188446	0.0942228	+	0.995551i	$0.469963\pi$
$332$	40.5243	2.22406
$333$	−5.91375	−0.324071
$334$	21.6569	1.18501
$335$	8.36330	0.456936
$336$	0	0
$337$	−10.5664	−0.575590	−0.287795	−	0.957692i	$-0.592922\pi$
$337$	−10.5664	−0.575590	−0.287795	+	0.957692i	$0.592922\pi$
$338$	−29.4125	−1.59983
$339$	9.56831	0.519679
$340$	11.3591	0.616035
$341$	−44.3939	−2.40407
$342$	10.8690	0.587728
$343$	0	0
$344$	−11.3661	−0.612821
$345$	−7.01008	−0.377410
$346$	25.0399	1.34615
$347$	31.8587	1.71026	0.855131	−	0.518411i	$-0.173476\pi$
$347$	31.8587	1.71026	0.855131	+	0.518411i	$0.173476\pi$
$348$	−27.6160	−1.48037
$349$	−25.8775	−1.38519	−0.692595	−	0.721327i	$-0.743533\pi$
$349$	−25.8775	−1.38519	−0.692595	+	0.721327i	$0.743533\pi$
$350$	0	0
$351$	0.224777	0.0119977
$352$	−30.4940	−1.62534
$353$	18.4633	0.982700	0.491350	−	0.870962i	$-0.336504\pi$
$353$	18.4633	0.982700	0.491350	+	0.870962i	$0.336504\pi$
$354$	14.2115	0.755331
$355$	12.9670	0.688214
$356$	−15.2527	−0.808393
$357$	0	0
$358$	22.8320	1.20671
$359$	6.71006	0.354143	0.177072	−	0.984198i	$-0.443338\pi$
$359$	6.71006	0.354143	0.177072	+	0.984198i	$0.443338\pi$
$360$	−2.63234	−0.138736
$361$	3.89911	0.205216
$362$	28.7134	1.50914
$363$	14.5349	0.762883
$364$	0	0
$365$	−4.86054	−0.254413
$366$	−14.9585	−0.781893
$367$	29.8477	1.55803	0.779017	−	0.627002i	$-0.215718\pi$
$367$	29.8477	1.55803	0.779017	+	0.627002i	$0.215718\pi$
$368$	−2.37621	−0.123869
$369$	−8.42429	−0.438551
$370$	13.4321	0.698300
$371$	0	0
$372$	−27.7523	−1.43889
$373$	30.7981	1.59466	0.797332	−	0.603542i	$-0.206244\pi$
$373$	30.7981	1.59466	0.797332	+	0.603542i	$0.206244\pi$
$374$	−41.2715	−2.13410
$375$	−1.00000	−0.0516398
$376$	27.6008	1.42340
$377$	−1.96504	−0.101205
$378$	0	0
$379$	0.995825	0.0511521	0.0255761	−	0.999673i	$-0.491858\pi$
$379$	0.995825	0.0511521	0.0255761	+	0.999673i	$0.491858\pi$
$380$	−15.1165	−0.775459
$381$	−10.5105	−0.538471
$382$	−48.7251	−2.49299
$383$	21.2275	1.08467	0.542336	−	0.840162i	$-0.317540\pi$
$383$	21.2275	1.08467	0.542336	+	0.840162i	$0.317540\pi$
$384$	−17.5231	−0.894222
$385$	0	0
$386$	−23.7228	−1.20746
$387$	−4.31788	−0.219490
$388$	−7.83946	−0.397988
$389$	7.69258	0.390029	0.195015	−	0.980800i	$-0.437525\pi$
$389$	7.69258	0.390029	0.195015	+	0.980800i	$0.437525\pi$
$390$	−0.510544	−0.0258524
$391$	−25.2073	−1.27479
$392$	0	0
$393$	15.4454	0.779116
$394$	−35.4066	−1.78376
$395$	−2.88942	−0.145382
$396$	15.9628	0.802160
$397$	−7.45223	−0.374017	−0.187008	−	0.982358i	$-0.559879\pi$
$397$	−7.45223	−0.374017	−0.187008	+	0.982358i	$0.559879\pi$
$398$	−42.9093	−2.15085
$399$	0	0
$400$	−0.338971	−0.0169485
$401$	−34.3128	−1.71350	−0.856749	−	0.515733i	$-0.827520\pi$
$401$	−34.3128	−1.71350	−0.856749	+	0.515733i	$0.827520\pi$
$402$	−18.9958	−0.947426
$403$	−1.97474	−0.0983687
$404$	−3.89359	−0.193713
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	−29.8834	−1.48126
$408$	−9.46554	−0.468614
$409$	36.1921	1.78958	0.894792	−	0.446482i	$-0.147323\pi$
$409$	36.1921	1.78958	0.894792	+	0.446482i	$0.147323\pi$
$410$	19.1344	0.944978
$411$	12.5738	0.620221
$412$	37.6348	1.85414
$413$	0	0
$414$	15.9222	0.782534
$415$	−12.8284	−0.629723
$416$	−1.35644	−0.0665050
$417$	−5.32111	−0.260576
$418$	54.9233	2.68639
$419$	−7.19173	−0.351339	−0.175670	−	0.984449i	$-0.556209\pi$
$419$	−7.19173	−0.351339	−0.175670	+	0.984449i	$0.556209\pi$
$420$	0	0
$421$	−13.8697	−0.675966	−0.337983	−	0.941152i	$-0.609745\pi$
$421$	−13.8697	−0.675966	−0.337983	+	0.941152i	$0.609745\pi$
$422$	46.3329	2.25545
$423$	10.4853	0.509812
$424$	0.950298	0.0461506
$425$	−3.59587	−0.174425
$426$	−29.4522	−1.42697
$427$	0	0
$428$	−2.85464	−0.137984
$429$	1.13585	0.0548392
$430$	9.80734	0.472952
$431$	4.00361	0.192847	0.0964235	−	0.995340i	$-0.469260\pi$
$431$	4.00361	0.192847	0.0964235	+	0.995340i	$0.469260\pi$
$432$	−0.338971	−0.0163087
$433$	3.65324	0.175564	0.0877819	−	0.996140i	$-0.472022\pi$
$433$	3.65324	0.175564	0.0877819	+	0.996140i	$0.472022\pi$
$434$	0	0
$435$	8.74218	0.419155
$436$	24.1876	1.15837
$437$	33.5453	1.60469
$438$	11.0399	0.527507
$439$	20.6705	0.986551	0.493276	−	0.869873i	$-0.335799\pi$
$439$	20.6705	0.986551	0.493276	+	0.869873i	$0.335799\pi$
$440$	−13.3017	−0.634136
$441$	0	0
$442$	−1.83585	−0.0873223
$443$	−24.0312	−1.14176	−0.570878	−	0.821035i	$-0.693397\pi$
$443$	−24.0312	−1.14176	−0.570878	+	0.821035i	$0.693397\pi$
$444$	−18.6812	−0.886570
$445$	4.82843	0.228889
$446$	−31.3610	−1.48499
$447$	10.6358	0.503054
$448$	0	0
$449$	34.1551	1.61188	0.805939	−	0.591999i	$-0.201661\pi$
$449$	34.1551	1.61188	0.805939	+	0.591999i	$0.201661\pi$
$450$	2.27133	0.107072
$451$	−42.5697	−2.00453
$452$	30.2257	1.42170
$453$	12.4885	0.586762
$454$	4.30097	0.201855
$455$	0	0
$456$	12.5965	0.589887
$457$	41.5623	1.94420	0.972100	−	0.234566i	$-0.0753670\pi$
$457$	41.5623	1.94420	0.972100	+	0.234566i	$0.0753670\pi$
$458$	−43.3167	−2.02406
$459$	−3.59587	−0.167841
$460$	−22.1444	−1.03249
$461$	−0.493631	−0.0229907	−0.0114953	−	0.999934i	$-0.503659\pi$
$461$	−0.493631	−0.0229907	−0.0114953	+	0.999934i	$0.503659\pi$
$462$	0	0
$463$	16.5087	0.767224	0.383612	−	0.923494i	$-0.374680\pi$
$463$	16.5087	0.767224	0.383612	+	0.923494i	$0.374680\pi$
$464$	2.96334	0.137570
$465$	8.78530	0.407409
$466$	42.9667	1.99039
$467$	13.8431	0.640581	0.320290	−	0.947319i	$-0.396220\pi$
$467$	13.8431	0.640581	0.320290	+	0.947319i	$0.396220\pi$
$468$	0.710059	0.0328225
$469$	0	0
$470$	−23.8155	−1.09853
$471$	−9.43208	−0.434607
$472$	16.4703	0.758106
$473$	−21.8191	−1.00325
$474$	6.56282	0.301440
$475$	4.78530	0.219565
$476$	0	0
$477$	0.361009	0.0165295
$478$	10.6023	0.484938
$479$	−18.2518	−0.833946	−0.416973	−	0.908919i	$-0.636909\pi$
$479$	−18.2518	−0.833946	−0.416973	+	0.908919i	$0.636909\pi$
$480$	6.03459	0.275440
$481$	−1.32928	−0.0606098
$482$	−62.4584	−2.84490
$483$	0	0
$484$	45.9148	2.08704
$485$	2.48167	0.112687
$486$	2.27133	0.103030
$487$	−6.14724	−0.278558	−0.139279	−	0.990253i	$-0.544478\pi$
$487$	−6.14724	−0.278558	−0.139279	+	0.990253i	$0.544478\pi$
$488$	−17.3360	−0.784765
$489$	8.04542	0.363826
$490$	0	0
$491$	−9.08171	−0.409852	−0.204926	−	0.978777i	$-0.565695\pi$
$491$	−9.08171	−0.409852	−0.204926	+	0.978777i	$0.565695\pi$
$492$	−26.6118	−1.19975
$493$	31.4357	1.41579
$494$	2.44311	0.109921
$495$	−5.05320	−0.227125
$496$	2.97796	0.133714
$497$	0	0
$498$	29.1376	1.30569
$499$	−13.2968	−0.595246	−0.297623	−	0.954683i	$-0.596194\pi$
$499$	−13.2968	−0.595246	−0.297623	+	0.954683i	$0.596194\pi$
$500$	−3.15894	−0.141272
$501$	9.53488	0.425987
$502$	3.68212	0.164341
$503$	−10.1771	−0.453774	−0.226887	−	0.973921i	$-0.572855\pi$
$503$	−10.1771	−0.453774	−0.226887	+	0.973921i	$0.572855\pi$
$504$	0	0
$505$	1.23256	0.0548483
$506$	80.4582	3.57680
$507$	−12.9495	−0.575106
$508$	−33.2022	−1.47311
$509$	−23.5875	−1.04550	−0.522749	−	0.852487i	$-0.675094\pi$
$509$	−23.5875	−1.04550	−0.522749	+	0.852487i	$0.675094\pi$
$510$	8.16740	0.361658
$511$	0	0
$512$	3.83013	0.169269
$513$	4.78530	0.211276
$514$	−18.4123	−0.812133
$515$	−11.9137	−0.524982
$516$	−13.6399	−0.600465
$517$	52.9843	2.33025
$518$	0	0
$519$	11.0243	0.483914
$520$	−0.591691	−0.0259473
$521$	−8.45280	−0.370324	−0.185162	−	0.982708i	$-0.559281\pi$
$521$	−8.45280	−0.370324	−0.185162	+	0.982708i	$0.559281\pi$
$522$	−19.8564	−0.869090
$523$	−13.5064	−0.590592	−0.295296	−	0.955406i	$-0.595418\pi$
$523$	−13.5064	−0.590592	−0.295296	+	0.955406i	$0.595418\pi$
$524$	48.7911	2.13145
$525$	0	0
$526$	−10.5190	−0.458650
$527$	31.5908	1.37612
$528$	−1.71289	−0.0745439
$529$	26.1412	1.13657
$530$	−0.819971	−0.0356173
$531$	6.25689	0.271526
$532$	0	0
$533$	−1.89359	−0.0820205
$534$	−10.9670	−0.474586
$535$	0.903670	0.0390690
$536$	−22.0151	−0.950905
$537$	10.0523	0.433788
$538$	15.0293	0.647959
$539$	0	0
$540$	−3.15894	−0.135939
$541$	−8.09084	−0.347852	−0.173926	−	0.984759i	$-0.555645\pi$
$541$	−8.09084	−0.347852	−0.173926	+	0.984759i	$0.555645\pi$
$542$	−28.7626	−1.23546
$543$	12.6417	0.542506
$544$	21.6996	0.930362
$545$	−7.65685	−0.327984
$546$	0	0
$547$	−18.1421	−0.775702	−0.387851	−	0.921722i	$-0.626782\pi$
$547$	−18.1421	−0.775702	−0.387851	+	0.921722i	$0.626782\pi$
$548$	39.7200	1.69675
$549$	−6.58579	−0.281075
$550$	11.4775	0.489402
$551$	−41.8339	−1.78219
$552$	18.4529	0.785408
$553$	0	0
$554$	25.3627	1.07756
$555$	5.91375	0.251025
$556$	−16.8091	−0.712863
$557$	−19.4308	−0.823308	−0.411654	−	0.911340i	$-0.635049\pi$
$557$	−19.4308	−0.823308	−0.411654	+	0.911340i	$0.635049\pi$
$558$	−19.9543	−0.844734
$559$	−0.970563	−0.0410504
$560$	0	0
$561$	−18.1706	−0.767165
$562$	58.9398	2.48623
$563$	−39.0971	−1.64775	−0.823874	−	0.566773i	$-0.808192\pi$
$563$	−39.0971	−1.64775	−0.823874	+	0.566773i	$0.808192\pi$
$564$	33.1224	1.39470
$565$	−9.56831	−0.402542
$566$	36.6288	1.53962
$567$	0	0
$568$	−34.1334	−1.43221
$569$	2.24133	0.0939613	0.0469806	−	0.998896i	$-0.485040\pi$
$569$	2.24133	0.0939613	0.0469806	+	0.998896i	$0.485040\pi$
$570$	−10.8690	−0.455252
$571$	3.45507	0.144590	0.0722952	−	0.997383i	$-0.476968\pi$
$571$	3.45507	0.144590	0.0722952	+	0.997383i	$0.476968\pi$
$572$	3.58807	0.150025
$573$	−21.4522	−0.896180
$574$	0	0
$575$	7.01008	0.292340
$576$	−13.0286	−0.542859
$577$	41.0091	1.70723	0.853616	−	0.520903i	$-0.174404\pi$
$577$	41.0091	1.70723	0.853616	+	0.520903i	$0.174404\pi$
$578$	−9.24375	−0.384489
$579$	−10.4445	−0.434057
$580$	27.6160	1.14669
$581$	0	0
$582$	−5.63670	−0.233649
$583$	1.82425	0.0755528
$584$	12.7946	0.529444
$585$	−0.224777	−0.00929340
$586$	50.8756	2.10165
$587$	−16.4192	−0.677692	−0.338846	−	0.940842i	$-0.610037\pi$
$587$	−16.4192	−0.677692	−0.338846	+	0.940842i	$0.610037\pi$
$588$	0	0
$589$	−42.0403	−1.73224
$590$	−14.2115	−0.585077
$591$	−15.5885	−0.641224
$592$	2.00459	0.0823881
$593$	33.4045	1.37176	0.685880	−	0.727714i	$-0.259417\pi$
$593$	33.4045	1.37176	0.685880	+	0.727714i	$0.259417\pi$
$594$	11.4775	0.470927
$595$	0	0
$596$	33.5978	1.37622
$597$	−18.8917	−0.773186
$598$	3.57895	0.146354
$599$	−15.7311	−0.642757	−0.321379	−	0.946951i	$-0.604146\pi$
$599$	−15.7311	−0.642757	−0.321379	+	0.946951i	$0.604146\pi$
$600$	2.63234	0.107465
$601$	0.156389	0.00637925	0.00318963	−	0.999995i	$-0.498985\pi$
$601$	0.156389	0.00637925	0.00318963	+	0.999995i	$0.498985\pi$
$602$	0	0
$603$	−8.36330	−0.340580
$604$	39.4505	1.60522
$605$	−14.5349	−0.590927
$606$	−2.79956	−0.113724
$607$	26.6825	1.08301	0.541505	−	0.840697i	$-0.317855\pi$
$607$	26.6825	1.08301	0.541505	+	0.840697i	$0.317855\pi$
$608$	−28.8774	−1.17113
$609$	0	0
$610$	14.9585	0.605652
$611$	2.35685	0.0953481
$612$	−11.3591	−0.459166
$613$	−29.6316	−1.19681	−0.598404	−	0.801194i	$-0.704198\pi$
$613$	−29.6316	−1.19681	−0.598404	+	0.801194i	$0.704198\pi$
$614$	−34.7825	−1.40371
$615$	8.42429	0.339700
$616$	0	0
$617$	29.9673	1.20644	0.603220	−	0.797575i	$-0.293884\pi$
$617$	29.9673	1.20644	0.603220	+	0.797575i	$0.293884\pi$
$618$	27.0601	1.08852
$619$	−3.31466	−0.133227	−0.0666137	−	0.997779i	$-0.521220\pi$
$619$	−3.31466	−0.133227	−0.0666137	+	0.997779i	$0.521220\pi$
$620$	27.7523	1.11456
$621$	7.01008	0.281305
$622$	10.7137	0.429579
$623$	0	0
$624$	−0.0761930	−0.00305016
$625$	1.00000	0.0400000
$626$	−48.7709	−1.94928
$627$	24.1811	0.965700
$628$	−29.7954	−1.18897
$629$	21.2650	0.847893
$630$	0	0
$631$	3.10223	0.123498	0.0617490	−	0.998092i	$-0.480332\pi$
$631$	3.10223	0.123498	0.0617490	+	0.998092i	$0.480332\pi$
$632$	7.60592	0.302547
$633$	20.3990	0.810789
$634$	−8.54240	−0.339262
$635$	10.5105	0.417098
$636$	1.14041	0.0452201
$637$	0	0
$638$	−100.338	−3.97243
$639$	−12.9670	−0.512965
$640$	17.5231	0.692661
$641$	−15.5926	−0.615871	−0.307936	−	0.951407i	$-0.599638\pi$
$641$	−15.5926	−0.615871	−0.307936	+	0.951407i	$0.599638\pi$
$642$	−2.05253	−0.0810070
$643$	17.9339	0.707244	0.353622	−	0.935388i	$-0.384950\pi$
$643$	17.9339	0.707244	0.353622	+	0.935388i	$0.384950\pi$
$644$	0	0
$645$	4.31788	0.170016
$646$	−39.0835	−1.53772
$647$	21.3559	0.839586	0.419793	−	0.907620i	$-0.362103\pi$
$647$	21.3559	0.839586	0.419793	+	0.907620i	$0.362103\pi$
$648$	2.63234	0.103408
$649$	31.6174	1.24109
$650$	0.510544	0.0200252
$651$	0	0
$652$	25.4150	0.995329
$653$	−5.44633	−0.213131	−0.106566	−	0.994306i	$-0.533985\pi$
$653$	−5.44633	−0.213131	−0.106566	+	0.994306i	$0.533985\pi$
$654$	17.3912	0.680052
$655$	−15.4454	−0.603501
$656$	2.85559	0.111492
$657$	4.86054	0.189628
$658$	0	0
$659$	−30.6743	−1.19490	−0.597451	−	0.801905i	$-0.703820\pi$
$659$	−30.6743	−1.19490	−0.597451	+	0.801905i	$0.703820\pi$
$660$	−15.9628	−0.621350
$661$	21.7555	0.846191	0.423095	−	0.906085i	$-0.360944\pi$
$661$	21.7555	0.846191	0.423095	+	0.906085i	$0.360944\pi$
$662$	7.78718	0.302657
$663$	−0.808269	−0.0313906
$664$	33.7688	1.31048
$665$	0	0
$666$	−13.4321	−0.520482
$667$	−61.2833	−2.37290
$668$	30.1201	1.16538
$669$	−13.8073	−0.533823
$670$	18.9958	0.733873
$671$	−33.2793	−1.28473
$672$	0	0
$673$	−11.9054	−0.458919	−0.229460	−	0.973318i	$-0.573696\pi$
$673$	−11.9054	−0.458919	−0.229460	+	0.973318i	$0.573696\pi$
$674$	−23.9998	−0.924440
$675$	1.00000	0.0384900
$676$	−40.9066	−1.57333
$677$	−14.8220	−0.569655	−0.284827	−	0.958579i	$-0.591936\pi$
$677$	−14.8220	−0.569655	−0.284827	+	0.958579i	$0.591936\pi$
$678$	21.7328	0.834643
$679$	0	0
$680$	9.46554	0.362987
$681$	1.89359	0.0725626
$682$	−100.833	−3.86111
$683$	−10.4028	−0.398053	−0.199026	−	0.979994i	$-0.563778\pi$
$683$	−10.4028	−0.398053	−0.199026	+	0.979994i	$0.563778\pi$
$684$	15.1165	0.577993
$685$	−12.5738	−0.480421
$686$	0	0
$687$	−19.0711	−0.727607
$688$	1.46364	0.0558006
$689$	0.0811467	0.00309144
$690$	−15.9222	−0.606148
$691$	−13.7129	−0.521664	−0.260832	−	0.965384i	$-0.583997\pi$
$691$	−13.7129	−0.521664	−0.260832	+	0.965384i	$0.583997\pi$
$692$	34.8252	1.32386
$693$	0	0
$694$	72.3616	2.74681
$695$	5.32111	0.201841
$696$	−23.0124	−0.872282
$697$	30.2926	1.14741
$698$	−58.7763	−2.22472
$699$	18.9170	0.715506
$700$	0	0
$701$	1.69903	0.0641715	0.0320857	−	0.999485i	$-0.489785\pi$
$701$	1.69903	0.0641715	0.0320857	+	0.999485i	$0.489785\pi$
$702$	0.510544	0.0192692
$703$	−28.2991	−1.06732
$704$	−65.8363	−2.48130
$705$	−10.4853	−0.394899
$706$	41.9362	1.57829
$707$	0	0
$708$	19.7652	0.742820
$709$	−19.1009	−0.717349	−0.358674	−	0.933463i	$-0.616771\pi$
$709$	−19.1009	−0.717349	−0.358674	+	0.933463i	$0.616771\pi$
$710$	29.4522	1.10532
$711$	2.88942	0.108362
$712$	−12.7101	−0.476330
$713$	−61.5857	−2.30640
$714$	0	0
$715$	−1.13585	−0.0424782
$716$	31.7545	1.18672
$717$	4.66788	0.174325
$718$	15.2408	0.568780
$719$	18.8550	0.703174	0.351587	−	0.936155i	$-0.385642\pi$
$719$	18.8550	0.703174	0.351587	+	0.936155i	$0.385642\pi$
$720$	0.338971	0.0126327
$721$	0	0
$722$	8.85617	0.329592
$723$	−27.4986	−1.02268
$724$	39.9343	1.48415
$725$	−8.74218	−0.324676
$726$	33.0135	1.22525
$727$	−51.6550	−1.91578	−0.957889	−	0.287139i	$-0.907296\pi$
$727$	−51.6550	−1.91578	−0.957889	+	0.287139i	$0.907296\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−11.0399	−0.408605
$731$	15.5265	0.574269
$732$	−20.8041	−0.768942
$733$	−29.4082	−1.08622	−0.543108	−	0.839663i	$-0.682752\pi$
$733$	−29.4082	−1.08622	−0.543108	+	0.839663i	$0.682752\pi$
$734$	67.7939	2.50232
$735$	0	0
$736$	−42.3030	−1.55931
$737$	−42.2615	−1.55672
$738$	−19.1344	−0.704345
$739$	38.9687	1.43349	0.716743	−	0.697337i	$-0.245632\pi$
$739$	38.9687	1.43349	0.716743	+	0.697337i	$0.245632\pi$
$740$	18.6812	0.686734
$741$	1.07563	0.0395142
$742$	0	0
$743$	−26.0247	−0.954754	−0.477377	−	0.878699i	$-0.658412\pi$
$743$	−26.0247	−0.954754	−0.477377	+	0.878699i	$0.658412\pi$
$744$	−23.1259	−0.847836
$745$	−10.6358	−0.389664
$746$	69.9526	2.56115
$747$	12.8284	0.469368
$748$	−57.4000	−2.09875
$749$	0	0
$750$	−2.27133	−0.0829373
$751$	−13.7211	−0.500690	−0.250345	−	0.968157i	$-0.580544\pi$
$751$	−13.7211	−0.500690	−0.250345	+	0.968157i	$0.580544\pi$
$752$	−3.55421	−0.129609
$753$	1.62113	0.0590772
$754$	−4.46326	−0.162542
$755$	−12.4885	−0.454504
$756$	0	0
$757$	−19.3747	−0.704185	−0.352093	−	0.935965i	$-0.614530\pi$
$757$	−19.3747	−0.704185	−0.352093	+	0.935965i	$0.614530\pi$
$758$	2.26185	0.0821540
$759$	35.4234	1.28579
$760$	−12.5965	−0.456924
$761$	21.3422	0.773655	0.386827	−	0.922152i	$-0.373571\pi$
$761$	21.3422	0.773655	0.386827	+	0.922152i	$0.373571\pi$
$762$	−23.8729	−0.864825
$763$	0	0
$764$	−67.7664	−2.45170
$765$	3.59587	0.130009
$766$	48.2146	1.74206
$767$	1.40641	0.0507825
$768$	−13.7435	−0.495927
$769$	−19.9554	−0.719609	−0.359805	−	0.933028i	$-0.617157\pi$
$769$	−19.9554	−0.719609	−0.359805	+	0.933028i	$0.617157\pi$
$770$	0	0
$771$	−8.10641	−0.291945
$772$	−32.9934	−1.18746
$773$	−10.0747	−0.362362	−0.181181	−	0.983450i	$-0.557992\pi$
$773$	−10.0747	−0.362362	−0.181181	+	0.983450i	$0.557992\pi$
$774$	−9.80734	−0.352518
$775$	−8.78530	−0.315577
$776$	−6.53260	−0.234507
$777$	0	0
$778$	17.4724	0.626416
$779$	−40.3128	−1.44436
$780$	−0.710059	−0.0254242
$781$	−65.5247	−2.34466
$782$	−57.2541	−2.04740
$783$	−8.74218	−0.312420
$784$	0	0
$785$	9.43208	0.336645
$786$	35.0816	1.25132
$787$	−43.8898	−1.56450	−0.782252	−	0.622962i	$-0.785929\pi$
$787$	−43.8898	−1.56450	−0.782252	+	0.622962i	$0.785929\pi$
$788$	−49.2431	−1.75421
$789$	−4.63121	−0.164875
$790$	−6.56282	−0.233495
$791$	0	0
$792$	13.3017	0.472657
$793$	−1.48034	−0.0525683
$794$	−16.9265	−0.600699
$795$	−0.361009	−0.0128037
$796$	−59.6778	−2.11522
$797$	12.1674	0.430991	0.215496	−	0.976505i	$-0.430863\pi$
$797$	12.1674	0.430991	0.215496	+	0.976505i	$0.430863\pi$
$798$	0	0
$799$	−37.7037	−1.33386
$800$	−6.03459	−0.213355
$801$	−4.82843	−0.170604
$802$	−77.9357	−2.75200
$803$	24.5613	0.866750
$804$	−26.4192	−0.931733
$805$	0	0
$806$	−4.48528	−0.157987
$807$	6.61695	0.232928
$808$	−3.24452	−0.114142
$809$	26.2485	0.922850	0.461425	−	0.887179i	$-0.347338\pi$
$809$	26.2485	0.922850	0.461425	+	0.887179i	$0.347338\pi$
$810$	−2.27133	−0.0798064
$811$	−25.2706	−0.887370	−0.443685	−	0.896183i	$-0.646329\pi$
$811$	−25.2706	−0.887370	−0.443685	+	0.896183i	$0.646329\pi$
$812$	0	0
$813$	−12.6633	−0.444122
$814$	−67.8750	−2.37902
$815$	−8.04542	−0.281819
$816$	1.21889	0.0426698
$817$	−20.6624	−0.722885
$818$	82.2043	2.87420
$819$	0	0
$820$	26.6118	0.929326
$821$	4.31464	0.150582	0.0752910	−	0.997162i	$-0.476011\pi$
$821$	4.31464	0.150582	0.0752910	+	0.997162i	$0.476011\pi$
$822$	28.5593	0.996121
$823$	−26.5105	−0.924099	−0.462050	−	0.886854i	$-0.652886\pi$
$823$	−26.5105	−0.924099	−0.462050	+	0.886854i	$0.652886\pi$
$824$	31.3610	1.09251
$825$	5.05320	0.175930
$826$	0	0
$827$	−2.85500	−0.0992782	−0.0496391	−	0.998767i	$-0.515807\pi$
$827$	−2.85500	−0.0992782	−0.0496391	+	0.998767i	$0.515807\pi$
$828$	22.1444	0.769572
$829$	−24.2187	−0.841151	−0.420575	−	0.907258i	$-0.638172\pi$
$829$	−24.2187	−0.841151	−0.420575	+	0.907258i	$0.638172\pi$
$830$	−29.1376	−1.01138
$831$	11.1665	0.387360
$832$	−2.92854	−0.101529
$833$	0	0
$834$	−12.0860	−0.418504
$835$	−9.53488	−0.329968
$836$	76.3867	2.64189
$837$	−8.78530	−0.303664
$838$	−16.3348	−0.564276
$839$	19.1152	0.659929	0.329965	−	0.943993i	$-0.392963\pi$
$839$	19.1152	0.659929	0.329965	+	0.943993i	$0.392963\pi$
$840$	0	0
$841$	47.4256	1.63537
$842$	−31.5026	−1.08565
$843$	25.9495	0.893747
$844$	64.4393	2.21809
$845$	12.9495	0.445475
$846$	23.8155	0.818795
$847$	0	0
$848$	−0.122372	−0.00420226
$849$	16.1266	0.553462
$850$	−8.16740	−0.280139
$851$	−41.4558	−1.42109
$852$	−40.9618	−1.40333
$853$	27.1889	0.930930	0.465465	−	0.885066i	$-0.345887\pi$
$853$	27.1889	0.930930	0.465465	+	0.885066i	$0.345887\pi$
$854$	0	0
$855$	−4.78530	−0.163654
$856$	−2.37877	−0.0813045
$857$	−14.9024	−0.509055	−0.254527	−	0.967066i	$-0.581920\pi$
$857$	−14.9024	−0.509055	−0.254527	+	0.967066i	$0.581920\pi$
$858$	2.57988	0.0880757
$859$	58.1880	1.98535	0.992674	−	0.120821i	$-0.0385527\pi$
$859$	58.1880	1.98535	0.992674	+	0.120821i	$0.0385527\pi$
$860$	13.6399	0.465118
$861$	0	0
$862$	9.09352	0.309727
$863$	−9.44406	−0.321480	−0.160740	−	0.986997i	$-0.551388\pi$
$863$	−9.44406	−0.321480	−0.160740	+	0.986997i	$0.551388\pi$
$864$	−6.03459	−0.205301
$865$	−11.0243	−0.374839
$866$	8.29773	0.281968
$867$	−4.06975	−0.138216
$868$	0	0
$869$	14.6008	0.495299
$870$	19.8564	0.673194
$871$	−1.87988	−0.0636974
$872$	20.1554	0.682549
$873$	−2.48167	−0.0839919
$874$	76.1926	2.57725
$875$	0	0
$876$	15.3542	0.518769
$877$	40.1876	1.35704	0.678519	−	0.734583i	$-0.262622\pi$
$877$	40.1876	1.35704	0.678519	+	0.734583i	$0.262622\pi$
$878$	46.9496	1.58447
$879$	22.3990	0.755501
$880$	1.71289	0.0577415
$881$	16.1706	0.544803	0.272401	−	0.962184i	$-0.412182\pi$
$881$	16.1706	0.544803	0.272401	+	0.962184i	$0.412182\pi$
$882$	0	0
$883$	−15.1917	−0.511242	−0.255621	−	0.966777i	$-0.582280\pi$
$883$	−15.1917	−0.511242	−0.255621	+	0.966777i	$0.582280\pi$
$884$	−2.55328	−0.0858760
$885$	−6.25689	−0.210323
$886$	−54.5827	−1.83374
$887$	−36.0916	−1.21184	−0.605919	−	0.795526i	$-0.707194\pi$
$887$	−36.0916	−1.21184	−0.605919	+	0.795526i	$0.707194\pi$
$888$	−15.5670	−0.522394
$889$	0	0
$890$	10.9670	0.367613
$891$	5.05320	0.169289
$892$	−43.6166	−1.46039
$893$	50.1752	1.67905
$894$	24.1573	0.807942
$895$	−10.0523	−0.336010
$896$	0	0
$897$	1.57571	0.0526113
$898$	77.5775	2.58879
$899$	76.8026	2.56151
$900$	3.15894	0.105298
$901$	−1.29814	−0.0432473
$902$	−96.6898	−3.21942
$903$	0	0
$904$	25.1870	0.837708
$905$	−12.6417	−0.420223
$906$	28.3656	0.942383
$907$	0.121978	0.00405021	0.00202510	−	0.999998i	$-0.499355\pi$
$907$	0.121978	0.00405021	0.00202510	+	0.999998i	$0.499355\pi$
$908$	5.98174	0.198511
$909$	−1.23256	−0.0408815
$910$	0	0
$911$	24.7082	0.818619	0.409310	−	0.912396i	$-0.365770\pi$
$911$	24.7082	0.818619	0.409310	+	0.912396i	$0.365770\pi$
$912$	−1.62208	−0.0537124
$913$	64.8247	2.14538
$914$	94.4016	3.12253
$915$	6.58579	0.217719
$916$	−60.2444	−1.99053
$917$	0	0
$918$	−8.16740	−0.269564
$919$	46.7825	1.54321	0.771606	−	0.636101i	$-0.219454\pi$
$919$	46.7825	1.54321	0.771606	+	0.636101i	$0.219454\pi$
$920$	−18.4529	−0.608374
$921$	−15.3137	−0.504604
$922$	−1.12120	−0.0369247
$923$	−2.91468	−0.0959378
$924$	0	0
$925$	−5.91375	−0.194443
$926$	37.4967	1.23222
$927$	11.9137	0.391299
$928$	52.7555	1.73178
$929$	−55.1614	−1.80979	−0.904893	−	0.425640i	$-0.860049\pi$
$929$	−55.1614	−1.80979	−0.904893	+	0.425640i	$0.860049\pi$
$930$	19.9543	0.654328
$931$	0	0
$932$	59.7576	1.95743
$933$	4.71691	0.154425
$934$	31.4422	1.02882
$935$	18.1706	0.594244
$936$	0.591691	0.0193400
$937$	−4.71006	−0.153871	−0.0769355	−	0.997036i	$-0.524514\pi$
$937$	−4.71006	−0.153871	−0.0769355	+	0.997036i	$0.524514\pi$
$938$	0	0
$939$	−21.4724	−0.700725
$940$	−33.1224	−1.08033
$941$	−25.0698	−0.817251	−0.408625	−	0.912702i	$-0.633992\pi$
$941$	−25.0698	−0.817251	−0.408625	+	0.912702i	$0.633992\pi$
$942$	−21.4234	−0.698011
$943$	−59.0550	−1.92309
$944$	−2.12091	−0.0690296
$945$	0	0
$946$	−49.5585	−1.61129
$947$	−17.6660	−0.574068	−0.287034	−	0.957920i	$-0.592669\pi$
$947$	−17.6660	−0.574068	−0.287034	+	0.957920i	$0.592669\pi$
$948$	9.12750	0.296447
$949$	1.09254	0.0354654
$950$	10.8690	0.352637
$951$	−3.76097	−0.121958
$952$	0	0
$953$	31.8233	1.03086	0.515429	−	0.856932i	$-0.327633\pi$
$953$	31.8233	1.03086	0.515429	+	0.856932i	$0.327633\pi$
$954$	0.819971	0.0265475
$955$	21.4522	0.694178
$956$	14.7456	0.476906
$957$	−44.1760	−1.42801
$958$	−41.4558	−1.33938
$959$	0	0
$960$	13.0286	0.420497
$961$	46.1815	1.48973
$962$	−3.01923	−0.0973438
$963$	−0.903670	−0.0291204
$964$	−86.8665	−2.79778
$965$	10.4445	0.336219
$966$	0	0
$967$	38.6054	1.24147	0.620733	−	0.784022i	$-0.286835\pi$
$967$	38.6054	1.24147	0.620733	+	0.784022i	$0.286835\pi$
$968$	38.2607	1.22975
$969$	−17.2073	−0.552778
$970$	5.63670	0.180983
$971$	36.8435	1.18236	0.591182	−	0.806538i	$-0.298662\pi$
$971$	36.8435	1.18236	0.591182	+	0.806538i	$0.298662\pi$
$972$	3.15894	0.101323
$973$	0	0
$974$	−13.9624	−0.447385
$975$	0.224777	0.00719864
$976$	2.23239	0.0714571
$977$	−22.2159	−0.710749	−0.355375	−	0.934724i	$-0.615647\pi$
$977$	−22.2159	−0.710749	−0.355375	+	0.934724i	$0.615647\pi$
$978$	18.2738	0.584332
$979$	−24.3990	−0.779796
$980$	0	0
$981$	7.65685	0.244465
$982$	−20.6276	−0.658252
$983$	−30.2284	−0.964136	−0.482068	−	0.876134i	$-0.660114\pi$
$983$	−30.2284	−0.964136	−0.482068	+	0.876134i	$0.660114\pi$
$984$	−22.1756	−0.706932
$985$	15.5885	0.496690
$986$	71.4008	2.27387
$987$	0	0
$988$	3.39785	0.108100
$989$	−30.2687	−0.962489
$990$	−11.4775	−0.364779
$991$	30.5294	0.969797	0.484899	−	0.874570i	$-0.338857\pi$
$991$	30.5294	0.969797	0.484899	+	0.874570i	$0.338857\pi$
$992$	53.0157	1.68325
$993$	3.42847	0.108799
$994$	0	0
$995$	18.8917	0.598907
$996$	40.5243	1.28406
$997$	−48.9769	−1.55111	−0.775557	−	0.631278i	$-0.782531\pi$
$997$	−48.9769	−1.55111	−0.775557	+	0.631278i	$0.782531\pi$
$998$	−30.2014	−0.956009
$999$	−5.91375	−0.187103

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.a.o.1.3	yes	4
3.2	odd	2		2205.2.a.bg.1.2		4
5.4	even	2		3675.2.a.bk.1.2		4
7.2	even	3		735.2.i.m.361.2		8
7.3	odd	6		735.2.i.n.226.2		8
7.4	even	3		735.2.i.m.226.2		8
7.5	odd	6		735.2.i.n.361.2		8
7.6	odd	2		735.2.a.n.1.3	✓	4
21.20	even	2		2205.2.a.bf.1.2		4
35.34	odd	2		3675.2.a.bl.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.a.n.1.3	✓	4	7.6	odd	2
735.2.a.o.1.3	yes	4	1.1	even	1	trivial
735.2.i.m.226.2		8	7.4	even	3
735.2.i.m.361.2		8	7.2	even	3
735.2.i.n.226.2		8	7.3	odd	6
735.2.i.n.361.2		8	7.5	odd	6
2205.2.a.bf.1.2		4	21.20	even	2
2205.2.a.bg.1.2		4	3.2	odd	2
3675.2.a.bk.1.2		4	5.4	even	2
3675.2.a.bl.1.2		4	35.34	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.a (trivial)

\(f(q)\)	\(=\)	\(q+2.27133 q^{2} +1.00000 q^{3} +3.15894 q^{4} -1.00000 q^{5} +2.27133 q^{6} +2.63234 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.27133 q^{2} +1.00000 q^{3} +3.15894 q^{4} -1.00000 q^{5} +2.27133 q^{6} +2.63234 q^{8} +1.00000 q^{9} -2.27133 q^{10} +5.05320 q^{11} +3.15894 q^{12} +0.224777 q^{13} -1.00000 q^{15} -0.338971 q^{16} -3.59587 q^{17} +2.27133 q^{18} +4.78530 q^{19} -3.15894 q^{20} +11.4775 q^{22} +7.01008 q^{23} +2.63234 q^{24} +1.00000 q^{25} +0.510544 q^{26} +1.00000 q^{27} -8.74218 q^{29} -2.27133 q^{30} -8.78530 q^{31} -6.03459 q^{32} +5.05320 q^{33} -8.16740 q^{34} +3.15894 q^{36} -5.91375 q^{37} +10.8690 q^{38} +0.224777 q^{39} -2.63234 q^{40} -8.42429 q^{41} -4.31788 q^{43} +15.9628 q^{44} -1.00000 q^{45} +15.9222 q^{46} +10.4853 q^{47} -0.338971 q^{48} +2.27133 q^{50} -3.59587 q^{51} +0.710059 q^{52} +0.361009 q^{53} +2.27133 q^{54} -5.05320 q^{55} +4.78530 q^{57} -19.8564 q^{58} +6.25689 q^{59} -3.15894 q^{60} -6.58579 q^{61} -19.9543 q^{62} -13.0286 q^{64} -0.224777 q^{65} +11.4775 q^{66} -8.36330 q^{67} -11.3591 q^{68} +7.01008 q^{69} -12.9670 q^{71} +2.63234 q^{72} +4.86054 q^{73} -13.4321 q^{74} +1.00000 q^{75} +15.1165 q^{76} +0.510544 q^{78} +2.88942 q^{79} +0.338971 q^{80} +1.00000 q^{81} -19.1344 q^{82} +12.8284 q^{83} +3.59587 q^{85} -9.80734 q^{86} -8.74218 q^{87} +13.3017 q^{88} -4.82843 q^{89} -2.27133 q^{90} +22.1444 q^{92} -8.78530 q^{93} +23.8155 q^{94} -4.78530 q^{95} -6.03459 q^{96} -2.48167 q^{97} +5.05320 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 8 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 8 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 8 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{8} + 4 q^{9} - 4 q^{10} + 8 q^{11} + 8 q^{12} - 4 q^{15} + 12 q^{16} + 8 q^{17} + 4 q^{18} - 8 q^{19} - 8 q^{20} + 12 q^{24} + 4 q^{25} + 4 q^{27} + 8 q^{29} - 4 q^{30} - 8 q^{31} + 28 q^{32} + 8 q^{33} - 8 q^{34} + 8 q^{36} + 8 q^{37} + 4 q^{38} - 12 q^{40} - 8 q^{43} - 16 q^{44} - 4 q^{45} + 12 q^{46} + 8 q^{47} + 12 q^{48} + 4 q^{50} + 8 q^{51} - 32 q^{52} + 8 q^{53} + 4 q^{54} - 8 q^{55} - 8 q^{57} - 24 q^{58} + 16 q^{59} - 8 q^{60} - 32 q^{61} - 20 q^{62} + 24 q^{64} + 24 q^{68} - 8 q^{71} + 12 q^{72} - 32 q^{74} + 4 q^{75} + 8 q^{76} - 12 q^{80} + 4 q^{81} - 8 q^{82} + 40 q^{83} - 8 q^{85} - 32 q^{86} + 8 q^{87} - 40 q^{88} - 8 q^{89} - 4 q^{90} - 8 q^{92} - 8 q^{93} - 16 q^{94} + 8 q^{95} + 28 q^{96} + 8 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 8 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^8 + 4 * q^9 - 4 * q^10 + 8 * q^11 + 8 * q^12 - 4 * q^15 + 12 * q^16 + 8 * q^17 + 4 * q^18 - 8 * q^19 - 8 * q^20 + 12 * q^24 + 4 * q^25 + 4 * q^27 + 8 * q^29 - 4 * q^30 - 8 * q^31 + 28 * q^32 + 8 * q^33 - 8 * q^34 + 8 * q^36 + 8 * q^37 + 4 * q^38 - 12 * q^40 - 8 * q^43 - 16 * q^44 - 4 * q^45 + 12 * q^46 + 8 * q^47 + 12 * q^48 + 4 * q^50 + 8 * q^51 - 32 * q^52 + 8 * q^53 + 4 * q^54 - 8 * q^55 - 8 * q^57 - 24 * q^58 + 16 * q^59 - 8 * q^60 - 32 * q^61 - 20 * q^62 + 24 * q^64 + 24 * q^68 - 8 * q^71 + 12 * q^72 - 32 * q^74 + 4 * q^75 + 8 * q^76 - 12 * q^80 + 4 * q^81 - 8 * q^82 + 40 * q^83 - 8 * q^85 - 32 * q^86 + 8 * q^87 - 40 * q^88 - 8 * q^89 - 4 * q^90 - 8 * q^92 - 8 * q^93 - 16 * q^94 + 8 * q^95 + 28 * q^96 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more